How the Seasons/Ages link works, if I remember correctly, is that after you beat one of the games you get a code for the other game. When you input this code it creates a new save file except you start with an extra health container and the wooden sword.
There are some other changes with this save file, and here are the ones I can remember off the top of my head:
- Whichever game you play second, you get some additional story that ties up both games and extra final bosses
- If you play Seasons second, you get some additional story regarding one of the Ages characters which I thought was quite nice; and supposedly if you beat Ages second there's an additional minigame based off Donkey Kong.
- You can transfer all of your rings from your first game to your second game
- Various characters in the second game will give you passwords to give to people in the first game, and they proceed to give you passwords you can tell Farore in the second game for benefits in both games, e.g. sword upgrades, another heart container, ring box upgrade, etc.
As you can see this means that whichever game you play second will probably end up being easier combat-wise and has a bunch of additional content. I did Ages -> Seasons and I think this is the better order, considering that base Ages has a decent amount of story compared to base Seasons and also you're more equipped to deal with the combat-based game. However, I do think Ages is the better game (my second favourite 2D Zelda) which would be a good reason to pick that second. Moreover, I've not actually done Seasons -> Ages yet so who knows.
Now, when you beat the second game, you get a code that you can input into the second game which creates a new save file so you can start the process in the opposite direction. Why you can't just start a new file is beyond me, but you do get a snazzy image for your file on the file select menu. I won't spoil what it is, though.